Waterflooding - II

7/26/2019 Waterflooding - II

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Waterflooding Part 2

Deepak

Devegowda

Improved Recovery Techniques


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Buckley

Leverett

Frontal

Advance Theory


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Objectives

Learn Buckley

Leverett

frontal advance

theory

Estimate oil recovery using the Buckley

-

Leverett

theory

Waterflood production forecasting using

frontal advance


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Motivation

Consider a one dimensional waterflood

Is the waterflood performance going to be

like

Yes, if gravity forces are stronger than

viscous or capillary forces


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Motivation

Or is the waterflood performance going to be

like this?


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Motivation

Typically waterflood performance is not

piston

-

like, instead it looks like:

The shape of the profile is predicted by

Buckley

Leverett

theory


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Waterflooding

Once you learn B-L theory, you will be able to

extend your knowledge to 2D and 3D

reservoirs

Understand the role of the various inputs on

the efficacy of the waterflood


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Model Description


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Model Description

At any point x, 2 phases (oil and water) may

flow

Assume incompressible fluids and that the

injection and production rates are constant


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Flow Equations


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Flow Equations

From the previous page, we can rewrite the

equations as


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Flow Equations

Subtracting eqn 1 and 2 from the previous

slide..


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Flow Equations

Now because we are only considering 2

phase flow

Substitute the expression above in to the

equation on the previous slide


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Flow Equations

We finally have.

and


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Fractional Flow

The fractional flow, fw is defined as:

So, the fractional flow becomes


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Fractional Flow

The final expression is:

When capillary pressure is negligible


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Assignment

Construct the fractional flow curve for the

data provided in the attached spreadsheet.


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Buckley Leverett Applications

Determine Sw vs distance for a 1D coreflood

Determine oil rate and recovery


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Model

Mass balance: Mass in Mass out =Accumulation


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Mass Balance for Water


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The mass balance gives us:

Assuming incompressible fluids:


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Sw is a function of time, t and distance, x.

Therefore:


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Saturation Tracking

Let us move with any arbitrarily chosen

saturation value

Along this plane, dSw = 0. Therefore the

equation on the previous page becomes:

Recall from 2 slides ago that


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Mass Balance

Combining the equations on the previous

slide, we get:


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Mass Balance

Since Qt is a constant and the fluids are

incompressible,

Differentiating this equation, we get:


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Velocity of the Front

Comparing the equations of the past 2 slides,

we get:

Where V(Sw) is the velocity of a front of

saturation, Sw.

All quantities on the RHS of the equation area constant, except dfw/dSw.


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Velocity of the Front

Therefore the velocity of the front is

proportional to dfw/dSw.


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Assignment

On the provided spreadsheet, construct the

curve, dfw/dSw.


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Saturation Profile

Integrating the frontal advance equation, we

get:

Because the flow is assumed incompressible,

the integral above is also just the total waterinjected, Wi.


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Saturation Profile

Now, we can plot the distance x travelled by a

saturation value, Sw


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Saturation Profile

This is clearly a physical impossibility you

cannot have 2 saturation values at the same x


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In Reality


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Flood Front Estimation


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Flood Front Estimation

Now

Or

Therefore where Swfis the

saturation at the front


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Flood Front

Graphically:


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Re-draw the Saturation Profile


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Oil Recovery at Breakthrough


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Oil Recovery at Breakthrough

Note, and

At breakthrough

Therefore


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Waterflooding Part 2

Deepak Devegowda

Improved Recovery Techniques

Date post:	13-Apr-2018
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Waterflooding - II

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